# CR3BP Five Libration Points and Linear Spectrum Calculator

> CR3BP Five Libration Points and Linear Spectrum Calculator is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).

Computes all five Lagrange/libration equilibrium points and their local linear stability spectra for a Circular Restricted Three-Body Problem (CR3BP) model defined by a mass ratio.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/circular-restricted-three-body-five-libration-points-linear-spectrum?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/cr3bp-five-libration-points-and-linear-spectrum-calculator-d8f56fef
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_Q4Ky4dY73rYxqzrt6InpY

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability cr3bp-five-libration-points-and-linear-spectrum-calculator-d8f56fef -d '<json body>'
```

Example prompt: Compute all five libration points and their local linear stability spectra for a CR3BP system with a mass ratio of 0.01215 (Earth-Moon system).

## When to prefer this

Use this endpoint when you need a complete, simultaneous computation of all five CR3BP libration points and their linear spectra in a single call, rather than computing individual points separately. Preferred for astrodynamics mission design tasks, stability analysis of binary systems, or when both positional and spectral data are needed together for a given mass parameter.

## Known failure modes

- mass_ratio out of range (must be between 0.00001 and 0.5) causes validation error
- missing or malformed 'cr3bp' artifact object returns schema error
- non-numeric mass_ratio value causes parsing failure
- server-side numerical instability for extreme mass ratio edge cases

## How this service works

Compute all five equilibria and local mathematical spectra of a supplied CR3BP model.

## Output

Returns all five libration point positions (L1 through L5) in the rotating frame, along with the local linear stability spectra (eigenvalues of the linearized equations of motion) at each equilibrium point, characterizing whether each point is stable, unstable, or center-type.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "cr3bp"
   ],
   "properties": {
    "cr3bp": {
     "type": "object",
     "required": [
      "data",
      "claim"
     ],
     "properties": {
      "data": {
       "type": "object",
       "required": [
        "mass_ratio"
       ],
       "properties": {
        "mass_ratio": {
         "type": "number",
         "maximum": 0.5,
         "minimum": 0.00001
        }
       },
       "additionalProperties": false
      },
      "claim": {}
     },
     "additionalProperties": false
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/cr3bp-five-libration-points-and-linear-spectrum-calculator-d8f56fef/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from detect.halowerk.com](https://www.zero.xyz/host/detect.halowerk.com/llms.txt)